Linked Questions

Why the central concepts of classical mechanics, viz. Lagrangian and Hamiltonian formalisms cannot address constraint forces like friction and others in dissipative systems?

Lagrangian formalism is a technique using which we can obtain the time evolution of a dynamical system. Given a dynamical system, can we say whether or not we can write down a Lagrangian (solving it ...

For physical systems with conservative forces, we can define a potential function $V$, and a Lagrangian $L=T-V$. At first, I thought that lagrangian mechanics only applied to systems with conservative ...

I was reading Herbert Goldstein's Classical Mechanics. Its first chapter explains holonomic and non-holonomic constraints, but I still don’t understand the underlying concept. Can anyone explain it to ...

We see variational principles coming into play in different places such as Classical Mechanics (Hamilton's principle which gives rise to the Euler-Lagrange equations), Optics (in the form of Fermat's ...

I am trying to write the Lagrangian and Hamiltonian for the forced Harmonic oscillator before quantizing it to get to the quantum picture. For EOM $$m\ddot{q}+\beta\dot{q}+kq=f(t),$$ I write the ...

A conservative force field is one in which all that matters is that a particle goes from point A to point B. The time (or otherwise) path involved makes no difference. Most force fields in physics ...

I am trying to understand how to use the Euler-Lagrange formulation when my system is subject to external forces. Consider the system pictured below: Let's define the lagrangian, as always, as $L =...

Can anyone give examples of mechanics problems which can be solved by Lagrange equations of the first kind, but not the second kind?

Consider the following question in classical mechanics Are Newton's Second Law, Hamilton's Principle and Lagrange Equations equivalent for particles and system of particles? If Yes, where ...

I've seen a few other threads on here inquiring about what is the point of Lagrange Multipliers, or the like. My main question though is, how can I tell by looking at a system in a problem that ...

When we enter into the scope of Analytical mechanics we usually start with these two primary notions: Lagrangian function & Hamiltonian function And usually textbooks define Lagrangian as $L=T-V$ ...

I'm pretty new to physics (I am presently taking AP Physics 1 though I am far ahead of that in math) and I was reading this paper that found the equations of motion for Atwood's machine using ...

I am going through the Goldstein book on classical mechanics and the after he derived the Lagrange equations he used Rayleigh dissipation function to include friction as a generalized force. In school ...

I'm studying Lagrangian mechanics, but I'm a little bit upset because when dealing with Lagrange's equations, we mostly consider conservative systems. If the system is non conservative they are very ...